Naive Approach 1: Say A, B, C are independent if P (A ∩B ∩C) = P (A)P (B)P (C). Suppose two six-sided dice are tossed and the outcome is noted. Let S denote the sample space of this experiment. i. Write down the set S explicitly. Consider the events A = {(i, i) : i = 1, 2, 3, 4, 5, 6}, B = {(x, y) : 7 ≤x + y ≤10}, C = {(x, y) : x + y is 2 or 7 or 8}. Write down the sets A, B, and C explicitly and calculate P (A), P (B), and P (C)

Q: A family plans to adopt three pets (one pet on Day 1, one on Day 2, and one on Day 3) and they want…

A: The sample space for their three pets is, S=CCC,CCD,CDC,DCC,CDD,DCD,DDC,DDD Thus, the sample space…

Q: Two fair coins are tossed (say a dime and a quarter). The two possible outcomes for a single coin…

A: we have to slove above question

Q: 4. Consider two events A and B in a sample space. If P(A) = 0.55, P(B) = 0.2, and P(A^B) = 0.08,…

A: A and B are two events in the same sample space. According to the addition formula the probabilities…

Q: A person pays $3 to roll two dice. He wins $9 if he gets ones on both dice, $6 if he gets the sum of…

A:

Q: In a study of recognition of the brand name Mrs. Fields cookies, out of the 50 adults in the study…

A: From the given information,out of 50 adults in the study, it was found that 35 recognized the brand…

Q: A three-dice is a six sided dice with only the numbers 1, 2 and 3. The usual numbers 4, 5 and 6 are…

A: Given that, A three-dice is a six sided dice with only the numbers 1, 2 and 3. The usual numbers 4,…

Q: Consider the following random experiment: you roll two dice whose faces have the labels 0, 0, 1, 1,…

A: (a) Sample Space:There are two dice, each with 3 possible outcomes (0, 1, or 2). So, the total…

Q: Let the S = {0,1,2,3,4,5,6,7,8,9,10} be the sample space of a random experiment. Suppose A is the…

A: The sample space is S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Q: A three-dice is a six sided dice with only the numbers 1, 2 and 3. The usual numbers 4, 5 and 6 are…

A:

Q: 10. A probability experiment is conducted in which the sample space of the experiment is S =…

A:

Q: A probability experiment is conducted in which the sample space of the experiment is S =…

A: The sample space is, S = {11,12,13,14,15,16,17,18,19,20,21,22}.

Q: An experiment is performed where an 8-sided die is rolled and then a coin is flipped. The possible…

A: From the provided information, The total outcomes after rolling a 8-sided and heads and tails for…

Q: Exercise 3. Suppose S is the sample space formed by rolling 3 fair, 6-sided dice and recordin the…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Suppose A and B are events in a sample space with P(A)=0.7, P(B)=0.48, P(B∪A)=0.88 answer the…

A: GIVEN DATA :  Two  events A & B in a sample space with PA=0.7, PB=0.48 and PB∪A=0.88       TO…

Q: 6. A pair of dice are rolled once (so will have two numbers show up when we roll the pair). The {(1,…

A: A pair of dice is  rolled once, then the sample space : Total number of outcomes = 36 Number of…

Q: 4. In a college, there are 150 students taking courses in Mathematics, Physics and Economics. Among…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: If you have the sample space of (5,6,7,8,9,10,11,12,13,14), what is the probability of getting a…

A: Sample space S= {5,6,7,8,9,10,11,12,13,14} n(S) = 10 numbers greater than 10 in S, denoted by E = {…

Q: Q1. A sample space consists of five simple events with Consider the events defined as follows Find…

A:

Q: An experiment is performed were in 6-sided die is rolled and then 3-color spinner is spun. The…

A: An experiment is performed were in 6-sided die is rolled and then 3-color spinner is spun. The…

Q: 6. An experiment is rolling two fair dice. Sample Space: {(1, 1), (1,2), (1, 3), (1,4), (1,5), (1,6)…

A: samples of dice getting sum 7 : (1,6) , (6,1) , (2,5) , (5, 2) , (3, 4), (4,3) (a) P(getting a sum…